Question: Simplify the following expression: $ a = \dfrac{-2t}{-7t + 4} + \dfrac{-5}{6} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-2t}{-7t + 4} \times \dfrac{6}{6} = \dfrac{-12t}{-42t + 24} $ Multiply the second expression by $\dfrac{-7t + 4}{-7t + 4}$ $ \dfrac{-5}{6} \times \dfrac{-7t + 4}{-7t + 4} = \dfrac{35t - 20}{-42t + 24} $ Therefore $ a = \dfrac{-12t}{-42t + 24} + \dfrac{35t - 20}{-42t + 24} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-12t + 35t - 20}{-42t + 24} $ $a = \dfrac{23t - 20}{-42t + 24}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-23t + 20}{42t - 24}$